New computing tools have allowed Peter Richardson, professor of engineering and physiology at Brown University, to test ideas about blood flow and clotting that he first proposed more than 30 years ago. His collaboration with mathematics colleagues Igor Pivkin and George Karniadakis resulted in a model that integrates fluid dynamics with platelet biochemistry and could provide new insights into the treatment and prevention of strokes and heart attacks.

PROVIDENCE, R.I. — Good science requires great
patience. In many fields, ideas and theories surge ahead while the tools to test
them can take decades to catch up. When Peter Richardson began talking with
colleagues who were modeling blood flow through the vessels on the heart’s
surface, he hardly suspected that the collaboration would lead to a test of
ideas he had proposed more than 30 years before.

The resulting model, described in the online edition of
Proceedings of the National Academy of Sciences appearing the week of
Oct. 30 to Nov. 3, could help evaluate candidate drugs aimed at preventing blood
clots – a major cause of strokes, heart attacks and organ transplant
rejection.

A model of platelets in action
Platelets that have been triggered (green spheres) can flow past clots of activated platelets (red spheres) before they become activated. The delay between triggering and activation helps explain a decrease in platelet aggregation at higher flow rates. Solid lines indicate flow paths; blue spheres are unactivated platelets.Image: Igor Pivkin

In 1970, Richardson, who had been working on the clotting
problems associated with artificial organs, saw a paper describing the time
course of clot formation in uninjured blood vessels. Gustav Born and his
co-author, Nicola Begent, had found an odd relationship – shaped like a
playground slide – between the rate of blood flow and the rate of blood
clot, or thrombus, formation. As blood flow increased, the rate at which the
clot grew increased rapidly, up to a point. After that point, the rate of growth
declined suddenly and then gradually flattened out.

Richardson recognized that there must be two groups of processes
at work – probably one chemical and one physical. The increase in clotting
with flow made sense. Faster blood flow meant more platelets encountered the
clot each second, so more had a chance to be captured by it. But the decrease
was puzzling.

Researchers knew that ADP (adenosine diphosphate) released from
injured tissue or existing thrombi could signal platelets to begin sticking
together at the site of the injury. Richardson proposed that a short delay
between triggering and activation could explain the decrease in aggregation with
increased blood flow. “If triggering is the time when the alarm goes
off,” said Richardson, a professor of engineering and physiology at Brown
University, “then activation is when your feet hit the floor.” As
blood flows faster, more platelets have already passed beyond the clot by the
time they are ready for action.

Richardson published his ideas at the time, but the computing
power needed to simulate more than 50,000 platelets and their individual
responses to a growing clot wasn’t yet available. Recently, when
co-authors Igor Pivkin and George Karniadakis sought Richardson’s input on
a similarly detailed simulation of blood flow in arteries on the heart’s
surface, the team realized that the time had come to test Richardson’s
hypothesis.

Pivkin and Karniadakis modified their model to fit
Richardson’s proposal and made hundreds of runs, changing flow rate,
activation time, and the strength of attraction between activated platelets.
Each set of runs produced a relationship between flow and aggregation remarkably
similar to what Begent and Born had found in hamsters.

While no recent experimental data set has the same detailed time
course as Begent and Born’s, Richardson and colleagues have found that
their model is able to reproduce several odd features of thrombus growth that
have been observed both in the laboratory and in tissue pathologies from
operating rooms and morgues. At high flow rates, they find the shape of the
thrombus goes from “hill-like” to “carpet-like.” At very
high flow rates and short activation times, they see secondary clots forming
downstream from the primary site.

The model is generalized in the sense that it does not require
many specific details, such as the concentration of fibrinogen (which binds
clots together) or the length of fibrinogen strands. It doesn’t need to
specifically calculate concentration or diffusion of the activation factor. Yet
it produces remarkably true-to-life results.

In the next few years, the team will refine the model by
incorporating molecular and sub-cellular details while enhancing the
representation of fluid dynamics and interactions between platelets and other
cells, working toward a truly multiscale model. Richardson also has
physiological experiments planned that will allow more rigorous testing and
refinement of the model.

Revisiting this line of inquiry, says Richardson, may lead
experimental researchers to explore drugs that could change the activation time
of platelets, leading to better preventive strategies for clots, whether they
result from blood vessel injury, atherosclerotic plaque or an artificial medical
device.

This work was supported by the National Science Foundation
Interagency Modeling and Analysis Group, and computations were performed at the
National Science Foundation supercomputing centers.